First of all, you surely do have a lot of incorrect grammar in your statement. I can't understand a word that you are asking.
Answer:
cos 30
Step-by-step explanation:
cos 30 + sin 60 / 1+ sin 30 + cos 60
= root3 / 2 + root3/2 / 1 + 1/2 + 1/2
= root 6/2 by 4/2
= root 6/4
= root 3/2
= cos 30
First, we are going to find the common ratio of our geometric sequence using the formula:
![r= \frac{a_{n}}{a_{n-1}}](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7Ba_%7Bn%7D%7D%7Ba_%7Bn-1%7D%7D%20)
. For our sequence, we can infer that
![a_{n}=-20](https://tex.z-dn.net/?f=a_%7Bn%7D%3D-20)
and
![a_{n-1}=4](https://tex.z-dn.net/?f=a_%7Bn-1%7D%3D4)
. So lets replace those values in our formula:
![r= \frac{-20}{4}](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B-20%7D%7B4%7D%20)
![r=-5](https://tex.z-dn.net/?f=r%3D-5)
Now that we have the common ratio, lets find the explicit formula of our sequence. To do that we are going to use the formula:
![a_{n}=a_{1}*r^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7B1%7D%2Ar%5E%7Bn-1%7D)
. We know that
![a_{1}=4](https://tex.z-dn.net/?f=a_%7B1%7D%3D4)
; we also know for our previous calculation that
![r=-5](https://tex.z-dn.net/?f=r%3D-5)
. So lets replace those values in our formula:
![a_{n}=4*(-5)^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3D4%2A%28-5%29%5E%7Bn-1%7D)
Finally, to find the 9th therm in our sequence, we just need to replace
![n](https://tex.z-dn.net/?f=n)
with 9 in our explicit formula:
![a_{9}=4*(-5)^{9-1}](https://tex.z-dn.net/?f=a_%7B9%7D%3D4%2A%28-5%29%5E%7B9-1%7D)
![a_{9}=4*(-5)^{8}](https://tex.z-dn.net/?f=a_%7B9%7D%3D4%2A%28-5%29%5E%7B8%7D)
![a_{9}=1562500](https://tex.z-dn.net/?f=a_%7B9%7D%3D1562500)
We can conclude that the 9th term in our geometric sequence is <span>
1,562,500</span>
Answer:
G
Step-by-step explanation: